Question

simplify.
\frac{3u^{2} - 21u}{8u^{2} - 56u}

Explanation:

Step1: Factor numerator and denominator

Factor out the greatest common factor (GCF) from the numerator \(3u^2 - 21u\) and the denominator \(8u^2 - 56u\).
For the numerator: The GCF of \(3u^2\) and \(-21u\) is \(3u\), so \(3u^2 - 21u = 3u(u - 7)\).
For the denominator: The GCF of \(8u^2\) and \(-56u\) is \(8u\), so \(8u^2 - 56u = 8u(u - 7)\).

Step2: Simplify the fraction

Now we have the fraction \(\frac{3u(u - 7)}{8u(u - 7)}\). Assuming \(u
eq 0\) and \(u
eq 7\) (to avoid division by zero), we can cancel out the common factors \(u\) and \((u - 7)\) from the numerator and the denominator.
After canceling, we get \(\frac{3}{8}\).

Answer:

\(\frac{3}{8}\)